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Modelling Population Growth
A colony of insects is being observed in the wild. After x weeks the number of insects, S, in the colony is given by
S = 20 e 0.56 x

The population after 12 weeks is (a whole number)
and the time for the population to reach 800 is weeks to 2 dps.

tickcross


Worked Solution:

After 12 weeks the population S is given by
S=20 e 0.56×12
=20 e 6.720
=20×828.81751
=16576.35
but we cannot have 0.35 insects
The population after 12 weeks is 16576 insects

To find x when S is 800:
S = 800=20 e 0.56×x
Divide both sides by 20:
40=e 0.56×x
Take natural logs of both sides:
ln(40)=0.56 x
3.689=0.56 x
6.587=x
The population reaches 800 in 6.59 weeks (to 2 dps)


A2 Pure Mathematics (MEI Structured Mathematics C3 C4) Third Edition (2004) pages 11-18
© MEI Produced by Dr Ron Knott, 1 September 2006
tom . button [AT] mei . org . uk 		Test reference: ExpModelling.html?ref=31870